Fibonacci Sequence Using Recursion In Java: Complete Explanation

Fibonacci sequence using Recursion in Java a is a popular real world problem which can easily be solved using any programming language such as Java, Python, C++ and more. Recursion method is a popular way of solving this fibonacci problem where the base cases are 0 and 1.

There are many different approaches to solving fibonacci sequences in Java which are iterative approach, recursive approach, memoization and dynamic programming. In this article, we will learn how to calculate the fibonacci series with the help of recursion in Java of a N given number.

Table of Contents

What is Fibonacci Sequence?

The Fibonacci Sequence is a series of numbers with each number is formed using the sum of the two preceding numbers in a given order. The simplest series in the fibonacci number is 1, 1, 2, 3, 5, 8, etc. The series in the fibonacci sequence starts with 0 and 1.

Fibonacci Sequence using recursion in java

Fibonacci Sequence Formula

The formula of the Fibonacci sequence using recursion in Java can be divided into two sections i,e. Base case and recursive approach. The fibonacci sequence using recursion depends on two major stages where the program repeatedly breaks down the problem into different parts until it reaches the base case.

Base Case: F(n) where n ==0 or n==1

Recursion Case: F(n) = F(n-1) + F(n-2) for n>1

We can use a recursion approach to get an efficient method of solving the factorial of a given number.

How Do We Approach Fibonacci Sequence Using Recursion?

Recursion can be used to solve a Fibonacci Problem using a simple two way approach. In the recursive approach we focus on calling the stack again and again and then backtracking each step progressively.

Fibonacci Sequence using recursion in java

In this approach we will use the base case as 0 and 1 when we get the value of the number as 0 we will return it with 0 and when the value will be 1 we will return it with 1 and then backtrack to reach the solution statement. We will keep calling the function again and again until we reach the base case.

Working of Recursive Approach in Fibonacci Sequence?

Recursion is a process which helps break down the problem into smaller subproblems and call itself with smaller values until it reaches the base case of the function. You can see the function calling in recursion to understand a little bit more about fibonacci series using recursion.

F(5) = F(4) + F(3)

= (F(3) + F(2)) + (F(2) + F(1))

= ((F(2) + F(1)) + F(2)) + (F(2) + F(1))

= (((F(1) + F(0)) + F(1)) + F(2)) + (F(2) + F(1))

= (((1 + 0) + 1) + (1 + 0)) + ((1 + 0) + 1)

= (1 + 1 + 1) + (1 + 1) + (1 + 1)

= 3 + 2 + 2

= 5

The above table shows the workflow of the recursive approach of fibonacci series. A simple representation in the workflow of the problem which can be used to solve the fibonacci problem using Java programming.

The function F(5) calls F(4) and F(3) similarly F(4) calls F(3) and F(2) and F(3) calls F(2) and F(1) in the function.
When the function reaches the base condition i,e. Either 0 or 1 then we will return 0 when the function n==0 and will return 1 when the function n==1.
Once the base case turns out we will backtrack every value and resolve the output for the following fibonacci series in reverse order.

Fibonacci Series Using Recursion In Java

Let us now get a fair insight of Recursive functions using recursion in Java.

public class FibonacciRecursion {

static int fibonacci(int n) {

if (n == 0) return 0; // Base case

if (n == 1) return 1; // Base case

return fibonacci(n – 1) + fibonacci(n – 2);

}

public static void main(String[] args) {

int n = 5;

System.out.println(“Fibonacci of ” + n + ” is: ” + fibonacci(n));

}

Why Recursion Using Java Is a Better Approach Than Loops?

Fibonacci Sequence using recursion in java

Recursion and loops are both methods of solving the fibonacci series using repetitive methods. However, sometimes recursion is a better approach in solving Java problems.

Recursive solutions are often shorter and easier to understand when compared to loops.
Recursion approach is suitable for problems like fibonacci series, factorial calculation, backtracking, tree traversals, etc.
Recursion fits for problems with trees and graph traversals.
Recursion is a better approach for backtracking problems.
With recursion we do not need to write the same program again and again at different places.

However, Recursion might not be a better approach for large inputs because of high memory usage which adds a new stack frame (O(n)) space complexity. The function execution in recursion is slower compared to loops in the program.

With too many recursive calls memory limits can be exceeded which will give rise to inefficiency in programming. Hence, we can use fibonacci sequence using recursion in java for selected number of questions in programming language.

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Fibonacci Sequence Using Recursion In Java FAQs

Q1. What is the Fibonacci Sequence?

Ans: The Fibonacci Sequence is a series of numbers with each number is formed using the sum of the two preceding numbers in a given order. The simplest series in the fibonacci number is 1, 1, 2, 3, 5, 8, etc. The series in the fibonacci sequence starts with 0 and 1.

Q2. Can we solve the Fibonacci Series using Recursion?

Ans: Yes, we can use the Fibonacci series using recursion to solve the problem efficiently. It uses a two step process where we declare the base case and logic for solving.

Q3. What is the space complexity for Recursive problems?

Ans: Fibonacci Series using recursive problems take a complexity of around O(n) due to the repeated call of stack in the problem. You can use it to achieve a fibonacci solution easily.

Q4. What is the disadvantage of Fibonacci Sequence using recursion?

Ans: When solving fibonacci problems for larger inputs the fibonacci series become inefficient and unsuitable which leads to high memory usage and slower execution of the program.